Invitation to Q-Series, An: From Jacobi's Triple Product Identity to Ramanujan's Most Beautiful Identity

ISBN-13: 9789814343848 / Angielski / Twarda / 2011 / 236 str.

Hei-Chi Chan

Opis

The aim of these lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan. Two central results in these notes are: (1) the evaluation of the Rogers-Ramanujan continued fraction — a result that convinced G H Hardy that Ramanujan was a “mathematician of the highest class”, and (2) what G. H. Hardy called Ramanujan's “Most Beautiful Identity”. This book covers a range of related results, such as several proofs of the famous Rogers-Ramanujan identities and a detailed account of Ramanujan's congruences. It also covers a range of techniques in q-series.